Equations · Finance and economics
Black–Scholes formula
The price of a European call option on a stock that pays no dividends.
C = S₀N(d₁) − Ke^(−rT)N(d₂)
Aethel says
C equals S sub zero N of d sub one, minus K e to the power of negative r T, times N of d sub two
What it says
The first term is the stock price weighted by a probability-like factor; the second is the strike price, discounted to today, weighted by the risk-neutral probability that the option ends in the money.
Here d₁ = (ln(S₀/K) + (r + σ²/2)T) / (σ√T) and d₂ = d₁ − σ√T, where σ is the stock's volatility.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| C | C | the call price |
| S₀ | S sub zero | today's stock price |
| K | K | the strike price |
| r, T | r, T | the risk-free rate and the time to expiry, in years |
| N(·) | N of | the cumulative standard normal distribution |
Where you meet it
Derivatives courses, the CFA and FRM curricula and trading desks.
Questions
How do you say Black–Scholes formula out loud?
C = S₀N(d₁) − Ke^(−rT)N(d₂) is read: “C equals S sub zero N of d sub one, minus K e to the power of negative r T, times N of d sub two.” That is exactly what Aethel says when it meets the formula in a book.
What does C mean in Black–Scholes formula?
C (said “C”) is the call price.
What does S₀ mean in Black–Scholes formula?
S₀ (said “S sub zero”) is today's stock price.
Can I listen to the equations in my own textbook like this?
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